What expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign?

A square shaped traffic sign is shown with length of one side labeled as 4x + 3.

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Below are the choices based on the question above:

16x2 + 12x + 9

  16x2 + 24x + 9

  8x2 + 9

  8x2 + 6

The answer is the second one 16x^2 +24x+9

Answer: [tex]\text{Area of the square shaped traffic sign }=16x^2+9+24x[/tex]

Step-by-step explanation:

Given: The side of the square shaped traffic sign = 4x+3

We know that the area of square is given by:-

[tex]Area= side^2[/tex]

Therefore, the area of the side of the square shaped field is given by:-

[tex]Area=(4x+3)^2[/tex]

We know that , [tex](a+b)^2=a^2+b^2+2ab[/tex]

Therefore,

[tex](4x+3)^2=(4x)^2+(3)^2+2(4x)(3)\\=16x^2+9+24x[/tex]

Hence, [tex]\text{Area of the square shaped traffic sign }=16x^2+9+24x[/tex]